We study the numerical approximation of SDEs with singular drifts (including distributions) driven by a fractional Brownian motion. Under the Catellier-Gubinelli condition that imposes the regularity of the drift to be strictly greater than $1-1/(2H)$, we obtain an explicit rate of convergence of a tamed Euler scheme towards the SDE, extending results for bounded drifts. Beyond this regime, when the regularity of the drift is $1-1/(2H)$, we derive a non-explicit rate. As a byproduct, strong well-posedness for these equations is recovered. Proofs use new regularising properties of discrete-time fBm and a new critical Gr\"onwall-type lemma. We present examples and simulations.

翻译：本文研究了由分数布朗运动驱动的具有奇异漂移（包括分布）的随机微分方程的数值逼近问题。在Catellier-Gubinelli条件下，即要求漂移项的正则性严格大于$1-1/(2H)$时，我们得到了驯服欧拉格式逼近该随机微分方程的显式收敛速率，从而推广了有界漂移情形的相关结果。当漂移项正则性为$1-1/(2H)$时，我们推导出了非显式收敛速率。作为推论，这些方程的强适定性得以恢复。证明过程利用了离散时间分数布朗运动的新正则化性质以及一个新的临界Gr\"onwall型引理。文中给出了具体算例与数值模拟结果。